Abstract
We investigate the impact of dissipation on the energy balance in the electron dynamics of metal clusters excited by strong electro-magnetic pulses. The dynamics is described theoretically by Time-Dependent Density-Functional Theory (TDDFT) at the level of Local Density Approximation (LDA) augmented by a self interaction correction term and a quantum collision term in Relaxation-Time Approximation (RTA). We evaluate the separate contributions to the total excitation energy, namely energy exported by electron emission, potential energy due to changing charge state, intrinsic kinetic and potential energy, and collective flow energy. The balance of these energies is studied as function of the laser parameters (frequency, intensity, pulse length) and as function of system size and charge. We also look at collisions with a highly charged ion and here at the dependence on the impact parameter (close versus distant collisions). Dissipation turns out to be small where direct electron emission prevails namely for laser frequencies above any ionization threshold and for slow electron extraction in distant collisions. Dissipation is large for fast collisions and at low laser frequencies, particularly at resonances.
Graphical abstract
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1140%2Fepjd%2Fe2017-80067-0/MediaObjects/10053_2017_1815_Fig1_HTML.jpg)
Similar content being viewed by others
References
E.K.U. Gross, W. Kohn, Adv. Quant. Chem. 21, 255 (1990)
E.K.U. Gross, J.F. Dobson, M. Petersilka, Top. Curr. Chem. 181, 81 (1996)
M.A.L. Marques, N.T. Maitra, F.M.S. Nogueira, E.K.U. Gross, A. Rubio, Fundamentals of Time-Dependent Density Functional Theory, Lecture Notes in Physics (Springer-Verlag, Berlin, 2012), Vol. 837
J.W. Negele, Rev. Mod. Phys. 54, 913 (1982)
K.T.R. Davies, K.R.S. Devi, S.E. Koonin, M.R. Strayer, in Treatise on Heavy–Ion Physics, Compound System Phenomena, edited by D.A. Bromley (Plenum Press, New York, 1985), Vol. 3, p. 3
M. Bender, P.H. Heenen, P.G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)
G.F. Bertsch, R. Broglia, Oscillations in Finite Quantum Systems (Cambridge University Press, Cambridge, 1994)
P.G. Reinhard, E. Suraud, in Time-Dependent Density Functional Theory, Lecture Notes in Physics, edited by M.A.L. Marques, C.A. Ullrich, F. Nogueira (Springer, Berlin, 2006), Vol. 706, p. 391
T. Fennel, K.H. Meiwes-Broer, J. Tiggesbäumker, P.G. Reinhard, P.M. Dinh, E. Suraud, Rev. Mod. Phys. 82, 1793 (2010)
C. Golabek, C. Simenel, Phys. Rev. Lett. 103, 042701 (2009)
V.E. Oberacker, A.S. Umar, J.A. Maruhn, P.G. Reinhard, Phys. Rev. C 82, 034603 (2010)
P.G. Reinhard, C. Toepffer, Int. J. Mod. Phys. E 3, 435 (1994)
G.F. Bertsch, P.F. Bortignon, R.A. Broglia, Rev. Mod. Phys. 55, 287 (1983)
Y. Abe, S. Ayik, P.G. Reinhard, E. Suraud, Phys. Rep. 275, 49 (1996)
V.V. Sargsyan, G.G. Adamian, N.V. Antonenko, W. Scheid, H.Q. Zhang, Phys. Rev. C 85, 024616 (2012) [Erratum: Phys. Rev. C 85, 069903 (2012)]
D. Lacroix, S. Ayik, Eur. Phys. J. A 50, 95 (2014)
N.D. Fatti, R. Bouffanais, F. Valle, C. Flytzanis, Phys. Rev. Lett. 81, 922 (1998)
C. Voisin, D. Christofilos, N.D. Fatti, F. Vallée, B. Prövel, E. Cottancin, J. Lermé, M. Pellarin, M. Broyer, Phys. Rev. Lett. 85, 2200 (2000)
E.E.B. Campbell, K. Hansen, K. Hoffmann, G. Korn, M. Tchaplyguine, M. Wittmann, I.V. Hertel, Phys. Rev. Lett. 84, 2128 (2000)
M. Schmidt, R. Kusche, T. Hippler, J. Donges, W. Kronmüller, B. von Issendorff, H. Haberland, Phys. Rev. Lett. 86, 1191 (2001)
F. Fehrer, P.G. Reinhard, E. Suraud, Appl. Phys. A 82, 145 (2006)
M. Kjellberg, O. Johansson, F. Jonsson, A.V. Bulgakov, C. Bordas, E.E.B. Campbell, K. Hansen, Phys. Rev. A 81, 023202 (2010)
F. Chandezon, C. Guet, B.A. Huber, D. Jalabert, M. Maurel, E. Monnand, C. Ristori, J.C. Rocco, Phys. Rev. Lett. 74, 3784 (1995)
U. Näher, S. Björnholm, S. Frauendorf, F. Garcias, C. Guet, Phys. Rep. 285, 245 (1997)
J. Daligault, F. Chandezon, C. Guet, B.A. Huber, S. Tomita, Phys. Rev. A 66, 033205 (2002)
P.G. Reinhard, E. Suraud, Ann. Phys. 354, 183 (2015)
L.E. Reichl, A Modern Course in Statistical Physics (Wiley, New York, 1998)
C. Cercignani, in The Boltzmann Equation and Its Applications, Applied Mathematical Sciences (Springer, New York, 1988), Vol. 67
E.A. Uehling, G.E. Uhlenbeck, Phys. Rev. 43, 552 (1933)
G.F. Bertsch, S. Das Gupta, Phys. Rep. 160, 190 (1988)
D. Durand, E. Suraud, B. Tamain, Nuclear Dynamics in the Nucleonic Regime (Institute of Physics, London, 2000)
A. Domps, P.G. Reinhard, E. Suraud, Phys. Rev. Lett. 81, 5524 (1998)
T. Fennel, G.F. Bertsch, K.H. Meiwes-Broer, Eur. Phys. J. D 29, 367 (2004)
L.P. Kadanoff, G. Baym, Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems, Frontiers in Physics (Benjamin, New York, 1962)
P.L. Bhatnagar, E.P. Gross, M. Krock, Phys. Rev. 94, 1954 (511)
N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976)
D. Pines, P. Nozières, The Theory of Quantum Liquids (W. A. Benjamin, New York, 1966)
A. Dutta, C. Trefzger, K. Sengupta, Phys. Rev. B 86, 085140 (2012)
P. Krause, T. Klamroth, P. Saalfrank, J. Chem. Phys. 127, 034107 (2007)
P.G. Reinhard, E. Suraud, Ann. Phys. 216, 98 (1992)
E. Suraud, P.G. Reinhard, New J. Phys. 16, 063066 (2014)
L. Lacombe, P.G. Reinhard, P.M. Dinh, E. Suraud, J. Phys. B 49, 245101 (2016)
C. Legrand, E. Suraud, P.G. Reinhard, J. Phys. B 35, 1115 (2002)
P. Klüpfel, P.M. Dinh, P.G. Reinhard, E. Suraud, Phys. Rev. A 88, 052501 (2013)
F. Calvayrac, P.G. Reinhard, E. Suraud, C.A. Ullrich, Phys. Rep. 337, 493 (2000)
P.G. Reinhard, E. Suraud, Introduction to Cluster Dynamics (Wiley, New York, 2004)
S. Kümmel, M. Brack, P.G. Reinhard, Eur. Phys. J. D 9, 149 (1999)
J.P. Perdew, Y. Wang, Phys. Rev. B 45, 13244 (1992)
B. Montag, P.G. Reinhard, Phys. Lett. A 193, 380 (1994)
B. Montag, P.G. Reinhard, Z. Phys. D 33, 265 (1995)
K.T.R. Davies, S.E. Koonin, Phys. Rev. C 23, 2042 (1981)
M.D. Feit, J.A. Fleck, A. Steiger, J. Comp. Phys. 47, 412 (1982)
V. Blum, G. Lauritsch, J.A. Maruhn, P.G. Reinhard, J. Comp. Phys. 100, 364 (1992)
P.G. Reinhard, P.D. Stevenson, D. Almehed, J.A. Maruhn, M.R. Strayer, Phys. Rev. E 73, 036709 (2006)
R.M. Dreizler, E.K.U. Gross, Density Functional Theory: An Approach to the Quantum Many-Body Problem (Springer-Verlag, Berlin, 1990)
J. Köhn, R. Redmer, K.H. Meiwes-Broer, T. Fennel, Phys. Rev. A 77, 033202 (2008)
J. Köhn, R. Redmer, T. Fennel, New J. Phys. 14, 055011 (2012)
R. Cusson, P.G. Reinhard, J. Maruhn, W. Greiner, M. Strayer, Z. Phys. A 320, 475 (1985)
C.A. Ullrich, J. Mol. Struct. (THEOCHEM) 501–502, 315 (2000)
P.G. Reinhard, O. Genzken, M. Brack, Ann. Phys. 5, 1 (1996)
J. Babst, P.G. Reinhard, Z. Phys. D 42, 209 (1997)
R. Loudon, The Quantum Theory of Light (Oxford Science Publications, Oxford, 2009)
L.V. Keldysh, Sov. Phys. J. Exp. Theor. Phys. 20, 1307 (1965)
P.G. Reinhard, F. Calvayrac, C. Kohl, S. Kümmel, E. Suraud, C.A. Ullrich, M. Brack, Eur. Phys. J. D 9, 111 (1999)
B. Montag, P.G. Reinhard, J. Meyer, Z. Phys. D 32, 125 (1994)
M. Brack, Rev. Mod. Phys. 65, 677 (1993)
M. Brack, R.K. Bhaduri, Semiclassical Physics (Addison-Wesley, Reading, 1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Dynamics of Systems at the Nanoscale”, edited by Andrey Solov’yov and Andrei Korol.
Rights and permissions
About this article
Cite this article
Vincendon, M., Suraud, E. & Reinhard, PG. Dissipation and energy balance in electronic dynamics of Na clusters. Eur. Phys. J. D 71, 179 (2017). https://doi.org/10.1140/epjd/e2017-80067-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2017-80067-0